Fluorescence correlation spectroscopy and photon count histograms in small domains. Part I: General theory

Analysis of fluctuations arising as fluorescent particles pass through a focused laser beam has enabled quantitative characterization of molecular kinetic processes. The mathematical frameworks of both fluorescence correlation spectroscopy (FCS) and photon counting histogram (PCH) analysis, which can measure these fluctuations, assume an infinite Gaussian beam, which prevents their application to particles within domains bounded at the nanoscale. We therefore derived general forms of FCS and PCH for bounded systems. The finite domain form of FCS differs from the classical form in its boundary and initial conditions and requires development of a new Fourier space solution for fitting data. Our finite-domain FCS predicts simulated data accurately and reduces to a previous model for the special case of molecules confined by two boundaries under Gaussian beams. Our approach enables estimation of the concentration of diffusing fluorophores within a finite domain for the first time. The method opens the possibility of quantification of kinetics in several systems for which this has never been possible, including in the one-dimensional lipid tubules discussed in Part 2 of this paper. Statement of SignificanceMethods based on fluorescence measurements of molecular concentration fluctuations, including Fluorescence Correlation Spectroscopy and Photon Count Histogram analysis, are widely used to determine rates of diffusion, chemical reaction and sizes of molecular aggregates. Typically, the range over which the molecules can diffuse is large compared to the size of the focused laser beam that excites the fluorescence. This work extends these measurements to systems that are comparable in size to the excitation laser beam. This extends the application of these methods to very small samples such as the interior of bacterial cells or the diffusion of molecules along individual macromolecules such as DNA.